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Double parton scattering at high energies

We discuss a few examples of rich newly developing field of double parton scattering. We start our presentation from production of two pairs of charm quark-antiquark and argue that it is the golden reaction to study the double parton scattering effects. In addition to the DPS we consider briefly also mechanism of single parton scattering and show that it gives much smaller contribution to the $c \bar c c \bar c$ final state. Next we discuss a perturbative parton-splitting mechanism which should be included in addition to the conventional DPS mechanism. We show that the presence of this mechanism unavoidably leads to collision energy and other kinematical variables dependence of so-called $σ_{eff}$ parameter being extracted from different experiments. Next we briefly discuss production of four jets. We concentrate on estimation of the contribution of DPS for jets remote in rapidity. Understanding of this contribution is very important in the context of searches for BFKL effects known under the the name Mueller-Navelet jets. We discuss the situation in a more general context. Finally we briefly mention about DPS effects in production of $W^+ W^-$. Outlook closes the presentation.